Magnetic Resonance Imaging: Physical Principles Lewis Center for NeuroImaging , Physics of MRI, An Overview  Nuclear Magnetic Resonance – Nuclear spins – Spin precession and the Larmor equation – Static B0 – RF excitation – RF detection  Spatial Encoding – Slice selective excitation – Frequency encoding – Phase encoding – Image reconstruction 08/13/20  Fourier Transforms – Continuous Fourier Transform – Discrete Fourier Transform – Fourier properties – k-space representation in MRI Physics of MRI  Echo formation – Vector summation – Phase dispersion – Phase refocus  2D Pulse Sequences – Spin echo – Gradient echo – Echo-Planar Imaging 08/13/20  Medical Applications – Contrast in MRI – Bloch equation  Tissue properties – T1 weighted imaging – T2 weighted imaging – Spin density imaging  Examples  3D Imaging  Spectroscopy Many spins in a voxel: vector summation spins in step spins not in step Rotating frame Lamor precession 08/13/20 Phase dispersion due to perturbing B fields Spin Phase φ ∝ γ Bt B = B0 + δB0 + δBcs + δBpp sampling Immediately after RF excitation 08/13/20 sometime after RF excitation Refocus spin phase – echo formation Echo Time (TE) • Invert perturbing field: δB Phase δBt (gradient echo, k-space sampling) • Invert spin state: Phase (spin echo) 08/13/20 δBt -δB φ-δB(t-TE/2) φ -φ -φ+δB(t-TE/2) time 0 Spin Echo  Spins dephase with time  Rephase spins with a 180° pulse  Echo time, TE  Repeat time, TR  (Running analogy) E q u ilib riu m P u lse t= S p in D e p h a s in g S p in e c h o t= T E 08/13/20 P u lse t= T E /2 Frequency encoding - 1D imaging Spatial-varying resonance frequency during RF detection B = B0 + Gxx S(t) ~ eiγ Βt S(t) ~ ∫ m(x)eiγ Gxxtdx m(x) x S(t) = ∫ m(x)eikxxdx = S(kx), 08/13/20 kx = γ Gxt m(x) = FT{S(kx)} Slice selection Spatial-varying resonance frequency during RF excitation ω ω = ω0 + γ Gzz B1 freq band z Excited location Slice profile m+ = mx+imy ~ γ ∫ b1(t)e-iγ Gzztdt = B1(γ Gzz) 08/13/20 Gradient Echo FT imaging 35000 Amplitude (arb) x Gradient ky -35000 Amplitude (arb) 35000 Readout y Gradient -35000 Amplitude (arb) 35000 kx z Gradient γ k (t ) = G (t )dt ∫ 2π -35000 Amplitude (arb) 35000 RF -35000 2000 4000 Time (us) 6000 08/13/20 8000 10000 Repeat with different phase-encoding amplitudes to fill k-space 10 Contrast, Imaging Parameters S(TR , TE ) ∝ ρ(1 − e or ρ(1 − e − TR / T1 − TR / T1 )e )e − TE / T2 − TE / T2* (SE ) (GRE) TE TR Image Weighting Short Long Proton Short Short T1 * Long Long T2, T2 08/13/20 21 Properties of Body Tissues Tissue T1 (ms) T2 (ms) Grey Matter (GM) 950 100 White Matter (WM) 600 80 Muscle 900 50 Cerebrospinal Fluid (CSF) 4500 2200 Fat 250 60 Blood 1200 100-200 MRI has high contrast for different tissue types! 08/13/20 22 MRI of the Brain - Sagittal T1 Contrast TE = 14 ms TR = 400 ms 08/13/20 T2 Contrast TE = 100 ms TR = 1500 ms Proton Density TE = 14 ms TR = 1500 ms 23 MRI of the Brain - Axial T1 Contrast TE = 14 ms TR = 400 ms 08/13/20 T2 Contrast TE = 100 ms TR = 1500 ms Proton Density TE = 14 ms TR = 1500 ms 24 Brain - Sagittal Multislice T1 08/13/20 25 Brain - Axial Multislice T1 08/13/20 26 Brain Tumor T1 Post-Gd T1 08/13/20 T2 27 3D Imaging  Instead of exciting a thin slice, excite a thick slab and phase encode along both ky and kz  Greater signal because more spins contribute to each acquisition  Easier to excite a uniform, thick slab than very thin slices  No gaps between slices  Motion during acquisition can be a problem 08/13/20 28 2D Sequence (Gradient Echo) ky acq Gx Gy kx Gz b1 TE TR 08/13/20 Scan time = NyTR 29 3D Sequence (Gradient Echo) acq Gx kz Gy Gz kx b1 08/13/20 ky Scan time = NyNzTR 30 3D Imaging - example •Contrast-enhanced MRA of the carotid arteries Acquisition time ~25s •160x128x32 acquisition (kxkykz) •3D volume may be reformatted in post-processing Volume-ofinterest rendering allows a feature to be isolated •More on contrast-enhanced MRA later 08/13/20 31 Spectroscopy  Precession frequency depends on the chemical environment (δBcs) e.g Hydrogen in water and hydrogen in fat have a ∆f = fwater – ffat = 220 Hz  Single voxel spectroscopy excites a small (~cm3) volume and measures signal as f(t) Different frequencies (chemicals) can be separated using Fourier transforms  Concentrations of chemicals other than water and fat tend to be very low, so signal strength is a problem  Creatine, lactate and NAA are useful indicators of tumor types 08/13/20 32 Spectroscopy - Example Intensity 08/13/20 Frequency 33 Future lectures  Magnetization preparation (phase and magnitude, pelc)  Fast imaging (fast sequences, epi, spiral…)  Motion (artifacts, compensation, correction,  Perfusion and diffusion  Functional imaging (fMRI)  Cardiac imaging (coronary MRA) navigator…)  MR angiography (TOF, PC, CE) 08/13/20 34 3rd dimension – phase encoding Before frequency encoding and after slice selection, apply y-gradient pulse that makes spin phase varying linearly in y Repeat RF excitation and detection with different gradient area S(ky, t) = ∫ ∫ (∫ m+(x,y,z)dz)eikyyeiγ Gxxtdxdy 08/13/20 35 ... Matter (GM) 95 0 100 White Matter (WM) 600 80 Muscle 90 0 50 Cerebrospinal Fluid (CSF) 4500 2200 Fat 250 60 Blood 1200 100-200 MRI has high contrast for different tissue types! 08/13/20 22 MRI of the... disabled during RF – Don’t get central “echo” data time 90 RF 08/13/20 18 Spin echo (SE) MR signal e-t/T2 e-t/T2* time 90 RF 08/13/20 180 RF 19 MR Parameters: TE and TR  Echo time, TE is the time... Transform – Discrete Fourier Transform – Fourier properties – k-space representation in MRI Physics of MRI  Echo formation – Vector summation – Phase dispersion – Phase refocus  2D Pulse Sequences